A heater of 220, V heats a volume of water in | vedclass

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(D) The heat energy $H$ required to heat a volume of water is constant.The heat produced by a heater is given by $H = \frac{V^2}{R} t$, where $V$ is t

Vedclass · Accepted Answer

$20$

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(D) The heat energy $H$ required to heat a volume of water is constant.The heat produced by a heater is given by $H = \frac{V^2}{R} t$, where $V$ is the voltage, $R$ is the resistance of the heater, and $t$ is the time.Since the same volume of water is heated, the heat required $H$ is the same in both cases.Assuming the resistance $R$ of the heater remains constant, we have $H = \frac{V_1^2}{R} t_1 = \frac{V_2^2}{R} t_2$.Given $V_1 = 220\, V$, $t_1 = 5\, 	ext{min}$, and $V_2 = 110\, V$.Substituting the values: $\frac{220^2}{R} 	imes 5 = \frac{110^2}{R} 	imes t_2$.$t_2 = 5 	imes \left( \frac{220}{110} ight)^2 = 5 	imes (2)^2 = 5 	imes 4 = 20\, 	ext{min}$.

$A$ heater of $220\, V$ heats a volume of water in $5\, \text{min}$ time. $A$ heater of $110\, V$ heats the same volume of water in ............... $\text{min}$.

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